Clustering and Nonnegative Matrix Factorization: A Mathematical and Algorithmic Perspective

Clustering is a fundamental task in machine learning and data analysis, enabling the discovery of inherent patterns within data. Nonnegative Matrix Factorization (NMF) has emerged as a powerful tool for clustering due to its ability to learn parts-based, interpretable representations. This article explores the theoretical foundations of clustering and NMF, their synergy, algorithmic formulations, and practical implementations. Experimental validation on synthetic data demonstrates the effectiveness of NMF-based clustering without using libraries such as sklearn or tensorflow.